Of course, here at Statalist we know, but others may disagree. So as another
source I turned to the Merriam-Webster Second Edition, 1949, which is
probably the last prescriptive dictionary at hand, wherein I find:
polychotomous [poly+chotomous as in dichotomous] Dividing,....
I know, I know, wrong side of the Atlantic and all that, .....
(silly colonials!) but maybe it is too late to stop the purported
malformation. Plus, I prefer the sound of polychotomous.
m.p.
Nick Cox wrote:

The OED works on descriptive, not prescriptive, principles,
so does not even purport to judge on correctness.
Nick
n.j.cox@durham.ac.uk
Marcello Pagano

If it is good enough for the Oxford English Dictionary,
it is good enough for me:

*1858* MAYNE
<http://dictionary.oed.com.ezp2.harvard.edu/help/bib/oed2-m2.h
tml#mayne>
/Expos. Lex./, /Polychotomus/, applied to a body that is
divided into numerous articulations..: polychotomous. *
1887* /Amer. Naturalist/ Oct. 915 Polychotomy is probably never more
than provisional, and all classification will eventually be
dichotomous.

So until we eventually reach the dichotomy where some of us
are right and some of us are wrong, let's allow polychotomous.

m.p.

Nick Cox wrote:

My only advice is marginal to your main question.

The term "polychotomous", although common in the
literature, is malformed and based on a misparsing
of the word "dichotomous", whose elements
are "dicho" and "tomous". The term "polytomous",
also common in the literature, is more nearly correct.
Help stamp out this linguistic monstrosity!
Nick
n.j.cox@durham.ac.uk
N.B. this is a different kind of argument from
those in favour of "heteroskedasticity" rather than
"heteroscedasticity". In the latter case, there are
plenty of precedents for rendering the Greek letter
kappa into the English letter c, so one could be
sceptical about that argument.
"polychotomous" just got into the literature because someone
didn't understand the etymology of "dichotomy" and other people
copied that mistake. It's still wrong.